Centripetal acceleration/ angular velocity question

AI Thread Summary
The discussion revolves around calculating the angular speed required for a circular space station to simulate Earth's gravity for its occupants. The diameter of the station is given as 52.5 meters, leading to a radius of approximately 8.356 meters. The user initially calculated the linear speed using the formula for centripetal acceleration, arriving at a value of 9.0538 m/s. However, they later realized they mistakenly used the diameter instead of the radius in their calculations. This highlights the importance of careful attention to detail in physics problems.
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This is my first post on here so let me know if I need to provide more info.

Homework Statement


A proposed space station includes living quarters in a circular ring 52.5 m in diameter. At what angular speed should the ring rotate so the occupants feel that they have the same weight as they do on Earth?

Homework Equations


r=c/2Pi
a(centripetal)= v2/r => v=sqrt( ac*r
Δ∅=s/r

The Attempt at a Solution


r=52.5/2*Pi= 8.356
v= sqrt(9.81*8.356)=9.0538
Δ∅=9.0538/8.356=1.084 rad/sec

This was my first attempt at the problem but I was returned that the answer is wrong, any ideas on what I did?
 
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Just kidding I realized I confused the diameter with the circumference, of course it's always the little things...
 

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